Question

An entrepreneur estimates that the total profit (profit = total revenue minus total cost) from his proposed company will be given by the function P(x) = x3 – 4x2 + 3x – 12, where P is in hundreds of dollars and x is the number of years elapsed after the company starts operations. In how many years (x) will the company break even (no profit, no loss)?

a) 1 year b) 2 year c) 3 year d) 4 year e) 6 year

Answer 1

hmm.. what you want to do here is trial and error :)
So if the company breaks even, there will be no profit and no loss meaning that p(x) will = 0 .
So basically you want to substitute in the values of x into p(x) and try to achieve 0.
When you do, that's how you'll know how many years it takes for there to be no profit and no loss.
So e.g.
For year 1, substitute x = 1 into p(x) = x^3 – 4x^2 + 3x – 12
Therefore p(1) = (1)^3 - 4(1)^2 + 3(1) - 12 = -12
therefore since p(1) = -12, this means in year 1, there will be a loss of 12.
Does that make sense?
:) so for the next one you'll sub in x = 2 so find p(2).

Our aim is to get P(x) = 0 :)

Answer 2

thanks I am going to try

Answer 3

The correct answer (D 4 years

Answer 4

yes that is correct.
Because if you input x = 4
We get p(4) = 4^3 – 4(4)^2 + 3(4) – 12
p(4) = 64 - 64 + 12 - 12
p(4) = 0.
That's why it took 4 years :)